Simplify the following expression: $\dfrac{56a^4}{48a^3}$ You can assume $a \neq 0$.
Solution: $ \dfrac{56a^4}{48a^3} = \dfrac{56}{48} \cdot \dfrac{a^4}{a^3} $ To simplify $\frac{56}{48}$ , find the greatest common factor (GCD) of $56$ and $48$ $56 = 2 \cdot 2 \cdot 2 \cdot 7$ $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(56, 48) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{56}{48} \cdot \dfrac{a^4}{a^3} = \dfrac{8 \cdot 7}{8 \cdot 6} \cdot \dfrac{a^4}{a^3} $ $\phantom{ \dfrac{56}{48} \cdot \dfrac{4}{3}} = \dfrac{7}{6} \cdot \dfrac{a^4}{a^3} $ $ \dfrac{a^4}{a^3} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a \cdot a} = a $ $ \dfrac{7}{6} \cdot a = \dfrac{7a}{6} $